This is the 11003rd most frequent Russian word.
гардинам
"Гардинам" is the dative plural form of "гардина," meaning "curtain" (specifically, a type of drape).
In this sentence, 'гардинам' is in the dative case, showing the relationship of the action (attaching clips) to the curtains.
Я повесил новые зажимы к гардинам.
I attached new clips to the curtains.
Here, 'гардинам' represents the location related to where the patterns are visible, in the dative case.
На гардинам появились красивые узоры.
Beautiful patterns appeared on the curtains.
The word 'гардинам' in the dative case shows the matching or correspondence direction between the furniture and the curtains.